"...swords were named after thier place of production, or at least supposed place of production. There were qala'i from a site in central Arabia or Iraq or Malaysia, Diyafi swords from Iraq, Baylamani from Baylaman which was either in Yemen or India and Mushrafi, from a site which was also either in Yemen or Syria. It is a curious characteristic of these names that the places are so uncertain , which suggests that even by the earliest Islamic times the names referred to types rather than places of production".
"The Armies of the Caliphs"
Hugh Kennedy, N.Y. 2001 p.173

With Islamic swords, they were of course held in the highest reverence, much the same as in European parlance from the swords of the Vikings into the age of chivalry. There was great attention put toward the steel in the blade and its forging, and the Arabs often used metaphoric and poetic descriptions, such as "...the sword drank the water" (op.cit. p.174) referring to the tempering. In the 9th century, al-Kindi, in his treatise on swords was particularly interested in the patterning in the steel in the blades, often using the term 'jauhar' (=jewel) in referencing watered steel.

After discovering the metallurgic nature seeming to be associated with the references to Tizona and Colada, it is interesting to consider the possibility that these name/terms might have been applied to more than these two swords alone. While the passage I have quoted clearly refers to the Islamic practice of naming swords, the culture in which El Cid lived and fought was in Moorish Spain, and the practice would seem to have been well in place. The references to the swords in later literary references to El Cid may well have reiterated the names or terms applied to his swords in earlier accounts.

Perhaps later references reflecting swords in inventories included swords called by the term (?) and not distinctly 'the' Tizona or 'Colada' (?)
I am only suggesting this as a possibility that should be considered in references to these resources, emphasizing this is only a thought.

In the study of often seen sword markings, it has been suggested that the 'makers' names inscribed or stamped in the blades such as 'ANDREA FERARA' or 'SAHAGUM' may well be brands or types of swords. This thought pertains to the superb marketing and commercialism of Solingen in using favored names of earlier makers to appeal to certain client groups. In earlier times, the Franks were also keenly aware of quality marking, and the famed and mysterious 'ULFBERHT' swords seem to have been marked in this sense as well.